应用功的互等定理求解四角点支承板的弯曲问题  

Application of Reciprocal Theorem of Work in Bending of Rectangular Plates Supported at Four Corners

作　　者：陈英杰[1,2] 刘焕庭 崔鹏 CHEN Yingjie;LIU Huanting;CUI Peng(Key Laboratory of Green Construction and Intelligent Operation and Maintenance of Civil Engineering in Hebei Province,Yanshan University,Qinhuangdao 066004,Hebei,China;College of Architectural Engineering and Mechanics,Yanshan University,Qinhuangdao 066004,Hebei,China)

机构地区：[1]燕山大学河北省土木工程绿色建造与智能运维重点实验室,河北秦皇岛066004 [2]燕山大学建筑工程与力学学院,河北秦皇岛066004

出　　处：《力学季刊》2022年第4期982-991,共10页Chinese Quarterly of Mechanics

基　　金：河北省土木工程绿色建造与智能运维重点实验室资助项目。

摘　　要：近年来,国内混凝土平板无梁楼盖体系坍塌事故频发,由此引发对以混凝土平板无梁楼盖体系为代表的四角点支承矩形板弯曲问题的思考.本文采用功的互等定理对四角点支承矩形板的弯曲问题进行求解,分别推导四角点支承矩形板在均布荷载、均布力矩和线性分布荷载作用下的挠曲面方程和执行方程,然后将不同载荷作用下所求得的挠度值与Ansys有限元模拟值进行对比分析.结果表明:该方法求解四角点支承矩形板弯曲问题通用有效;为以无梁楼盖为代表的四角点支承矩形板弯曲问题的求解提供了一种新方法,具有相当的实用价值.In recent years, the collapse accidents of concrete slab beamless floor system occurred frequently in China, causing much attention to the bending problem of the rectangular plate supported by four corners represented by the concrete slab beamless floor system. In this paper, the reciprocal theorem of work is used to solve the bending problem of rectangular plate supported at four corners. The deflection surface equation and the execution equation of rectangular plate supported at four corners under the uniform load, the uniform moment and the linear distribution load are derived respectively. Then, the deflection results obtained under different loads are compared with the Ansys finite element simulation results. It shows that the proposed method is universal and effective in solving the bending problem of rectangular plate supported at four corners, providing a new approach for solving the bending problem of rectangular plate supported at four corners represented by the beamless floor. This work has considerable value of engineering application.

关 键 词：矩形板 角点支承 功的互等定理 挠曲面方程 执行方程 

分 类 号：TU313[建筑科学—结构工程]